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§23.21(i) Classical Dynamics

In §22.19(ii) it is noted that Jacobian elliptic functions provide
a natural basis of solutions for problems in Newtonian classical dynamics with
quartic potentials in canonical form (1-x2)⁢(1-k2⁢x2). The
Weierstrass function ℘ plays a similar role for cubic potentials in
canonical form g3+g2⁢x-4⁢x3. See, for example,
Lawden (1989, Chapter 7) and
Whittaker (1964, Chapters 4–6).